Total Hamming Distance

class Solution(object):
    def totalHammingDistance(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        bin_num = ["{0:b}".format(num) for num in nums]
        zip_list = []
        for i in range(len(bin_num)):
            for k in zip(bin_num, bin_num[i:]):
                zip_list.append(k)
        count = 0
        len_list = []
        for x in zip_list:
            for i in range(2):
                len_list.append(len(x[i]))
        max_len = max(len_list)
        zip_c = []
        for c in zip_list:
            tuple_to_list = list(c)
            for i in range(2):
                if len(tuple_to_list[i]) < max_len:
                    byte_num = max_len-len(c[i])
                    tuple_to_list[i] = '0' * byte_num + str(tuple_to_list[i])
            zip_c.append(tuple_to_list)
        for new_c in zip_c:
                for j in range(max_len):
                    if new_c[0][j] != new_c[1][j]:
                        count = count+1
        return count

更简便如下：

def totalHammingDistance(self, nums):
    return sum(b.count('0') * b.count('1') for b in zip(*map('{:032b}'.format, nums)))

$\overline r_a + \frac{\sum_{b\in N}\quad  sim(a, b)*(r_{b, P}\qquad  - \overline  r_{\qquad b})}{\sum_{b\in  N} \quad sim(a, b)}$